Abstract:
The various mechanisms for neutrinoless double beta decay in gauge theories are reviewed and the present experimental data is used to set limits on physics scenarios beyond the standard model. The positive indications for nonzero neutrino masses in various experiments such as those involving solar, atmospheric and accelerator neutrinos are discussed and it is pointed out how some neutrino mass textures consistent with all data can be tested by the ongoing double beta decay experiments. Finally, the outlook for observable neutrinoless double beta decay signal in grand unified theories is discussed.

Abstract:
We discuss the results of a search for anomaly free Abelian Z_N discrete symmetries that lead to automatic R-parity conservation and prevents dangerous higher-dimensional proton decay operators in simple extensions of the minimal supersymmetric extension of the standard model (MSSM) based on the left-right symmetric group, the Pati-Salam group and SO(10). We require that the superpotential for the models have enough structures to be able to give correct symmetry breaking to MSSM and potentially realistic fermion masses. We find viable models in each of the extensions and for all the cases, anomaly freedom of the discrete symmetry restricts the number of generations.

Abstract:
We review various ways of obtaining consistency between the idea of supersymmetric grand unification and an apparent low value of $\alpha_s \sim 0.112$ indicated by several low energy experiments. We argue that to reconcile the low value of $\alpha_s$ with the predictions of supersymmetric GUTs, we need to go beyond the standard minimal supersymmetric GUT scenario and invoke new physics either at $10^{11}-10^{12}$ GeV, or at the GUT scale.

Abstract:
The $\eegg$ event reported recently by the CDF Collaboration has been interpreted as a signal of supersymmetry in several recent papers. In this article, we report on an alternative non-supersymmetric interpretation of the event using an extension of the standard model which contains new physics at the electroweak scale that does not effect the existing precision electroweak data. We extend the standard model by including an extra sequential generation of fermions, heavy right-handed neutrinos for all generations and an extra singly charged SU(2)-singlet Higgs boson. We discuss possible ways to discriminate this from the standard supersymemtric interpretations.

Abstract:
Recent experimental searches for neutrino mass in tritium beta decay yield a negative value for the mass-squared of the electron neutrino. If this effect is genuine, then it is hard to understand it using conventional particle physics ideas as embodied in the standard model or its simple extensions that have been widely discussed. We consider the possibility that there is a hidden anomalous long range interaction of neutrinos that is responsible for this effect and study the phenomenological consistency of this idea. We also discuss how such interactions may arise in extensions of the standard model.

Abstract:
We show that one of the ways of obtaining consistency between the idea of supersymmetric grand unification and an apparent low value of $\alpha_{strong}(M_Z)\simeq .11$ indicated by several low energy experiments is to have an intermediate scale corresponding to a local $B-L$ symmetry breaking around the mass scale of $10^{10}$ to $10^{12}$ GeV. We discuss the realization of this idea within the framework of supersymmetric $SO(10)$ grand unified theories with spectra of particles derivable from simple superstring-inspired versions of this model. We then study the $b-\tau$ mass unification within this class of models and show that due to the influence of new gauge and Yukawa interactions beyond the intermediate scale, the prediction of the $b$-quark mass comes out well within the presently accepted values. We also discuss an un-orthodox class of SUSY models inspired by some theoretical considerations having two pairs of Higgs doublets at low energy and show that they also can lead to unification with intermediate scales and low $\alpha_{s}(M_Z)$ as desired.

Abstract:
We analyze the minimal supersymmetric left-right model with non-re\-nor\-malizable interactions induced by higher scale physics and study its {\it CP} violating properties. We show that it: (i) solves the strong {\it CP} problem; (ii) predicts the neutron electric dipole moment well within experimental limits (thus solving the usual SUSY {\it CP} problem). In addition, it automatically conserves {\it R}-parity. The key points are that the parity symmetry forces the Yukawa couplings to be hermitean, while supersymmetry ensures that the scalar potential has a minimum with real higgs doublet vacuum expectation values. Gluino and B-L gaugino masses are automatically real. The observed {\it CP} violation in the kaon system comes, as in the Standard Model, from the Kobayashi-Maskawa-type phases. These solutions are valid for any value of the right-handed breaking scale $M_R$, as long as the effective theory below $M_R$ has only two Higgs doublets that couple fully to fermions. ({\it i.e.} the theory below $M_R$ is MSSM-like.) The potentially dangerous $SU(2)_L$ gaugino one-loop contributions to $\bar{\Theta}$ below $M_R$ can be avoided if the left-right symmetry originates from a unified theory in which the $SU(2)_{L,R}$ gaugino masses are real. As an example, we show how the left-right symmetry can be embedded in an SO(10) theory.

Abstract:
It is shown that the minimal supersymmetric left-right model can provide a natural solution to the strong {\it CP} problem without the need for an axion, nor any additional symmetries beyond supersymmetry and parity.

Abstract:
We present a new mechanism for doublet-triplet splitting in supersymmetric SO(10) models using a missing vev pattern which is different from the one used in the currently popular Dimopoulos-Wilczek method. In our method, the doublets in a {$\bf 16,\bar{16}$} pair are the ones split from the rest of the multiplet and are then mixed with the doublets from one or two {\bf 10}'s giving rise to the doublets {$\bf H_u$} and {$\bf H_d$} of the standard model. This approach provides a natural way to understand why top quark is so much heavier than the bottom quark. It also enables us to generate both hierarchical and nonhierarchical pattern for neutrino masses, the latter being of interest if neutrino is the hot component of the dark matter of the universe. We construct a simple, realistic model based on this idea. The model uses only simple representations, has no unwanted flat directions and maintains coupling constant unification as a prediction.

Abstract:
In minimal left-right symmetric models, the mass of the neutral Higgs field mediating tree-level flavor changing effects (FCNH) is directly related to the parity breaking scale. Specifically, the lower bound on the Higgs mass coming from Higgs-induced tree-level effects, and exceeding about 15 TeV, would tend to imply a W_R mass bound much higher than that required by gauge exchange loop effects -- the latter allowing W_R masses as low as 2.5 TeV. Since a W_R mass below 4 TeV is accessible at the LHC, it is important to investigate ways to decouple the FCNH effects from the W_R mass. In this paper, we present a model where this happens, providing new motivation for LHC searches for W_R in the 1 - 4 TeV mass range.